In my SharePoint I see that I have the Enterprise webparts such as chart, status list etc (http://www.sharepointconfig.com/2010/06/sharepoint-2010-web-parts-by-license-type/). Does me having this mean that we have purchased an Enterprise cal OR does it mean that I need to buy one? Is there a way you can turn off Enterprise features?
If you see these Web Parts, than yes, Enterprise was enabled in your farm. (I cannot answer if you have purchased it, but I do hope so :))
To turn of the Enterprise Site features:
This will disable it only for single site collection, and you will need to do it on another site collection if you do not need these.
Please note: You should not disable these features if someone is using these, as you might lose some data when deactivating.
To enable SharePoint Enterprise in first place, you need to enter an enterprise key via Central Administration. Once entered the farm will be upgraded to Enterprise and you cannot downgrade it back to Standard. In case you do not have proper licenses (every user needs to have an Enterprise CAL) you will need to disable the Enterprise features as I described above.
For some useful script to check where Enterprise features are running, and some other licensing FAQs, check this article.